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   <h1>Python Module Index</h1>

   <div class="modindex-jumpbox">
   <a href="#cap-p"><strong>p</strong></a>
   </div>

   <table class="indextable modindextable">
     <tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
     <tr class="cap" id="cap-p"><td></td><td>
       <strong>p</strong></td><td></td></tr>
     <tr>
       <td><img src="_static/minus.png" class="toggler"
              id="toggle-1" style="display: none" alt="-" /></td>
       <td>
       <a href="prml.html#module-prml"><code class="xref">prml</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.bayesnet.html#module-prml.bayesnet"><code class="xref">prml.bayesnet</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.bayesnet.html#module-prml.bayesnet.discrete"><code class="xref">prml.bayesnet.discrete</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.bayesnet.html#module-prml.bayesnet.probability_function"><code class="xref">prml.bayesnet.probability_function</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.bayesnet.html#module-prml.bayesnet.random_variable"><code class="xref">prml.bayesnet.random_variable</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.clustering.html#module-prml.clustering"><code class="xref">prml.clustering</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.clustering.html#module-prml.clustering.k_means"><code class="xref">prml.clustering.k_means</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.dimreduction.html#module-prml.dimreduction"><code class="xref">prml.dimreduction</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.dimreduction.html#module-prml.dimreduction.autoencoder"><code class="xref">prml.dimreduction.autoencoder</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.dimreduction.html#module-prml.dimreduction.bayesian_pca"><code class="xref">prml.dimreduction.bayesian_pca</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.dimreduction.html#module-prml.dimreduction.pca"><code class="xref">prml.dimreduction.pca</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel"><code class="xref">prml.kernel</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.gaussian_process_classifier"><code class="xref">prml.kernel.gaussian_process_classifier</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.gaussian_process_regressor"><code class="xref">prml.kernel.gaussian_process_regressor</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.kernel"><code class="xref">prml.kernel.kernel</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.polynomial"><code class="xref">prml.kernel.polynomial</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.rbf"><code class="xref">prml.kernel.rbf</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.relevance_vector_classifier"><code class="xref">prml.kernel.relevance_vector_classifier</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.relevance_vector_regressor"><code class="xref">prml.kernel.relevance_vector_regressor</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.kernel.html#module-prml.kernel.support_vector_classifier"><code class="xref">prml.kernel.support_vector_classifier</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear"><code class="xref">prml.linear</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.bayesian_logistic_regression"><code class="xref">prml.linear.bayesian_logistic_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.bayesian_regression"><code class="xref">prml.linear.bayesian_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.classifier"><code class="xref">prml.linear.classifier</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.emprical_bayes_regression"><code class="xref">prml.linear.emprical_bayes_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.fishers_linear_discriminant"><code class="xref">prml.linear.fishers_linear_discriminant</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.least_squares_classifier"><code class="xref">prml.linear.least_squares_classifier</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.linear_regression"><code class="xref">prml.linear.linear_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.logistic_regression"><code class="xref">prml.linear.logistic_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.perceptron"><code class="xref">prml.linear.perceptron</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.regression"><code class="xref">prml.linear.regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.ridge_regression"><code class="xref">prml.linear.ridge_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.softmax_regression"><code class="xref">prml.linear.softmax_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.variational_linear_regression"><code class="xref">prml.linear.variational_linear_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.linear.html#module-prml.linear.variational_logistic_regression"><code class="xref">prml.linear.variational_logistic_regression</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov"><code class="xref">prml.markov</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.categorical_hmm"><code class="xref">prml.markov.categorical_hmm</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.gaussian_hmm"><code class="xref">prml.markov.gaussian_hmm</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.hmm"><code class="xref">prml.markov.hmm</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.kalman"><code class="xref">prml.markov.kalman</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.particle"><code class="xref">prml.markov.particle</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.markov.html#module-prml.markov.state_space_model"><code class="xref">prml.markov.state_space_model</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.html#module-prml.nn"><code class="xref">prml.nn</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array"><code class="xref">prml.nn.array</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array.array"><code class="xref">prml.nn.array.array</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array.broadcast"><code class="xref">prml.nn.array.broadcast</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array.ones"><code class="xref">prml.nn.array.ones</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array.reshape"><code class="xref">prml.nn.array.reshape</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.array.html#module-prml.nn.array.zeros"><code class="xref">prml.nn.array.zeros</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.html#module-prml.nn.config"><code class="xref">prml.nn.config</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.distribution.html#module-prml.nn.distribution"><code class="xref">prml.nn.distribution</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.distribution.html#module-prml.nn.distribution.bernoulli"><code class="xref">prml.nn.distribution.bernoulli</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.distribution.html#module-prml.nn.distribution.categorical"><code class="xref">prml.nn.distribution.categorical</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.distribution.html#module-prml.nn.distribution.distribution"><code class="xref">prml.nn.distribution.distribution</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.distribution.html#module-prml.nn.distribution.gaussian"><code class="xref">prml.nn.distribution.gaussian</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.html#module-prml.nn.function"><code class="xref">prml.nn.function</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.image.html#module-prml.nn.image"><code class="xref">prml.nn.image</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.image.html#module-prml.nn.image.convolve2d"><code class="xref">prml.nn.image.convolve2d</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.image.html#module-prml.nn.image.deconvolve2d"><code class="xref">prml.nn.image.deconvolve2d</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.image.html#module-prml.nn.image.max_pooling2d"><code class="xref">prml.nn.image.max_pooling2d</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.image.html#module-prml.nn.image.util"><code class="xref">prml.nn.image.util</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.io.html#module-prml.nn.io"><code class="xref">prml.nn.io</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.io.html#module-prml.nn.io.io"><code class="xref">prml.nn.io.io</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.loss.html#module-prml.nn.loss"><code class="xref">prml.nn.loss</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.loss.html#module-prml.nn.loss.kl"><code class="xref">prml.nn.loss.kl</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.loss.html#module-prml.nn.loss.sigmoid_cross_entropy"><code class="xref">prml.nn.loss.sigmoid_cross_entropy</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.loss.html#module-prml.nn.loss.softmax_cross_entropy"><code class="xref">prml.nn.loss.softmax_cross_entropy</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.math.html#module-prml.nn.math"><code class="xref">prml.nn.math</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.math.html#module-prml.nn.math.add"><code class="xref">prml.nn.math.add</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.math.html#module-prml.nn.math.divide"><code class="xref">prml.nn.math.divide</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.math.html#module-prml.nn.math.exp"><code class="xref">prml.nn.math.exp</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
       <a href="prml.nn.math.html#module-prml.nn.math.log"><code class="xref">prml.nn.math.log</code></a></td><td>
       <em></em></td></tr>
     <tr class="cg-1">
       <td></td>
       <td>&#160;&#160;&#160;
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